The pirate ship swings guests back and forth, giving them a feeling of weightlessness. The boat is supported by four tubular uprights attached to a main axle, allowing it to swing in a pendulum motion.
Since the ship is a pendulum, it moves in simple harmonic motion.
Information On The Pirate Ship:
Riders per Ship: 54
Ship Length: 43 feet = 13.1 meters
Height of Ship in Full Swing: 66 feet = 20.1 meters
Total Ride Net Weight: 28 tons = 25401 kilograms
Velocity:
PE = KE
mgy = .5mv^2
gy = .5v^2
(9.8)(20.1) = .5v^2
v = 19.8 m/s
Period:
T = 7.9 s
Frequency: 1/ 7.9 = .127 cycles/s
Length of Middle Support Beam: (if there was one)
T = 2π (L / 9.8)^1/2
7.9 = 2π (L / 9.8)^1/2
L = 15.5 m
Acceleration:
a = 2 g
g = 9.8 m/s
a = 9.8 * 2 = 19.6 m/s downward
Energy of 87.1 kg person on board:
KE = .5mv^2
KE = (.5)(87.1)(19.8)^2
KE = 17073.4 J
Group Members: Clayton, Jake, John, and Joe
The pirate ship swings guests back and forth, giving them a feeling of weightlessness. The boat is supported by four tubular uprights attached to a main axle, allowing it to swing in a pendulum motion.
Since the ship is a pendulum, it moves in simple harmonic motion.
Information On The Pirate Ship:
Riders per Ship: 54
Ship Length: 43 feet = 13.1 meters
Height of Ship in Full Swing: 66 feet = 20.1 meters
Total Ride Net Weight: 28 tons = 25401 kilograms
Velocity:
PE = KE
mgy = .5mv^2
gy = .5v^2
(9.8)(20.1) = .5v^2
v = 19.8 m/s
Period:
T = 7.9 s
Frequency: 1/ 7.9 = .127 cycles/s
Length of Middle Support Beam: (if there was one)
T = 2π (L / 9.8)^1/2
7.9 = 2π (L / 9.8)^1/2
L = 15.5 m
Acceleration:
a = 2 g
g = 9.8 m/s
a = 9.8 * 2 = 19.6 m/s downward
Energy of 87.1 kg person on board:
KE = .5mv^2
KE = (.5)(87.1)(19.8)^2
KE = 17073.4 J
PE = mgy
PE = (87.1)(9.8)(20.1)
PE = 17157.0
Percent Difference: [(17157 - 17073.4) / ((17157 + 17073.4) / 2)] * 100 = 0.49 %